# How do you calculate  (tan^-1 (2)) ?

Aug 2, 2016

See explanation

#### Explanation:

Think about $\tan \left(\theta\right) = 2$

So $\theta = {\tan}^{- 1} \left(2\right)$

$\textcolor{b r o w n}{\text{So the question is really asking: What angle gives a tangent value of 2}}$

We know that $\tan \left(\theta\right) = \left(\text{opposite")/("adjacent}\right)$

So we can relate this condition to the right triangle:

Unfortunately this is not one of those triangles where $\theta$ is an easily identifiable whole number. So we can not state what it is just by looking at the ratio of the sides. So we need to look it up.

If using a scientific calculator make sure your calculator is set to degrees. If it is set to radians and you need the answer to be in degrees then multiply the radian answer by $\frac{180}{\pi}$.

You normally see a key with an orange or red $\textcolor{red}{{\text{tan}}^{- 1}}$ above it. Press the 'SHIFT' button then press the key with the ${\tan}^{- 1}$ above it. Enter the value 2 and then press the 'execute' key (or whatever key you normally press for an entered calculation to start).

$\textcolor{b l u e}{\text{I got "theta~~63.435" to 3 decimal places}}$

The $\approx$ means approximately equal to